The Projection of a space (2)

The matrix A projects the space in the direction  of the  eigenvector V3  on a plan  determined by the eigenvector V1 and V2 if : 

* The eigenvector V1 has its eigenvalue equal to  one and    
* The eigenvector V2 has its eigenvalue equal to  one and    
* The eigenvector V3 has its eigenvalue equal to zero and 

* If The vectors V1 and V2 and V3 are linearly independent 

In these examples, you choose the vectors of the plan and the vector for the projection. You compute  the matrix A that projects the space in the direction of the  eigenvector V3  onto a plan  determined by the eigenvectors V1 and V2. Next, you can calculate the projection of a point P onto the plan.

You can choose the vectors of the plan and the vector for the projection.

• c00a.c

You create the matrix A.

• c00b.c

You verify the properties of the matrix A.

• c00c.c

You can calculate the projection of a point P onto the plan.

• c00d.c

Check if the projection of a point P lies on the plane.

• c00e.c